Changes in images of brain functional activity that are produced by disease or by activation of various pathways in the normal brain can only be unambiguously interpreted if the rates of the physiological and biochemical processes that underlie the imaging method are quantified. In imaging modalities that use radioactive tracers, e.g. positron emission tomography (PET), quantification is carried out by means of a mathematical model that describes the rates of the biochemical reactions in the metabolic pathway of the tracer and traced molecules. Selection of the best kinetic model is critical as the use of an inappropriate model can lead to substantial errors in quantification and possible misinterpretation of results. Once a model is selected, numerical procedures that are efficient, robust, and require minimal assumptions about the errors in the measurements are required to estimate accurately the parameters. Additionally, powerful statistical tests are needed so that the data can be examined for significant differences among experimental groups. The objective of this project is to develop better techniques for addressing these interrelated mathematical and statistical issues; advances in the current year were made in the following three areas: (1) Work concluded on a method to estimate the number of true null hypotheses in multivariate analysis of neuroimaging data. In the repeated testing of a null univariate hypothesis in many sites, procedures are available to maintain the Type I error of the set of tests at a specified level. These methods assume a "global null hypothesis," i.e., that the statistics computed in each region or voxel are generated by null distributions. This may be too conservative when a significant proportion of the sites is affected by the experimental manipulation. We developed a rigorous statistical procedure for use with a previously reported graphical method for estimation of the number of true null hypotheses in the set of tests. This estimate can be used to sharpen existing multiple comparison procedures. (2) Examination of the impact of kinetic heterogeneity of tissues included in PET measurements on determinations of cerebral blood flow (CBF) with O-15 water and PET continued. The kinetic model currently used for measurement of CBF does not take heterogeneity into account. We have previously quantified the extent to which this leads to an underestimation of CBF with the kinetic model currently used, and developed a kinetic model that takes into account the heterogeneity and avoids the CBF underestimation. Due to the high degree of nonlinearity of the model in its parameters, however, estimation of the parameters with standard nonlinear least squares algorithms lacks robustness and is computationally intensive. We have developed an alternative algorithm that is both efficient and robust; it provides accurate estimates of weighted average blood flow in a heterogeneous tissue. We have also demonstrated in simulation studies that the algorithm can be used to provide accurate estimates of gray matter blood flow from the PET data themselves without the need of a co-registered structural image for correction of partial volume effects. We are currently testing this method on O-15 water PET data from studies of normal human subjects. (3) Work began on adapting the quantitative autoradiographic 14C-leucine method for determination of rates of local cerebral protein synthesis (CPS) for use in man with 11C-leucine and PET. In the 14C-leucine method in animals, brain tissue sections are washed in formalin and exposed to an air drying process. This removes 14C-leucine and 14C-carbon dioxide in the tissue and leaves only 14C-labeled proteins, whose concentration must be measured. PET measurements necessarily include all radioactivity in the field of view. When the method is adapted for PET the amounts of 11C-leucine and 11C-carbon dioxide in the tissue will be estimated through kinetic modeling. The parameters of the kinetic model will also be used as part of the determination of rates of regional CPS. Preliminary simulation studies have demonstrated the feasibility of the proposed kinetic modeling processes. Studies to validate the accuracy of the estimation as well as the determination of regional CPS will be carried out in animals.